Excuse me as I step up on my soap box.
To have an excellent high range, you must have an excellent low range.
That's right. Do you practice Rochuts down the octave? You want to be able to play the snot out of Bolero? Can you play it two octaves down?
"But I play tenor trombone, low notes are for the bass trombonists."
Very true. But there are several second trombone parts that randomly are playing lower than the third trombone. And the whole Saint-Seans solo is pretty low-note intense (still don't know why that isn't in the third part...). Don't be the tenor trombonist who disappoints the bass trombonist with some wimpy pedal B♭s. I have a story from grad school that should bring perspective.
While in grad school, Mark Lawrence^ would assign orchestral rep to sections to prepare and have ready for studio class the following week. This was a great way to learn repertoire, and Mark of course had tons of great insight and advice. One particular week I was in a section assigned Holst's Planets. Had tons of fun prepping all the music. We got to Friday studio class and started working through the material. Zorba* was playing principal trombone, and as we worked through Jupiter, Mark asked Zorba to play 12 bars before 4. Zorba is fine until the last three notes, a G#, F# and E at the bottom of the staff. None of those notes speak. Mark asks Zorba to do it again and to give extra focus to the last notes (it is also marked with a decrescendo.) Zorba air balls again. Mark asks for a third time. Same result. It is dead silence in the room. Mark sighs and informs Zorba that they should be spending way more time in the lower register and that it is inexcusable to be unprepared while their colleagues came prepared for studio class, and we moved on. That is the only time I ever saw Mark critique a player and not provide a positive silver lining to soften the blow.
So, if Mark Lawrence says low range is important, it means the low range is important. Get practicing them low notes!
* You can sure bet I changed this person's name.
^ Mark Lawrence is the retired principal trombonist of the San Francisco Symphony. He taught at SFCM until recently. Mark was Joe Alessi's first teacher. Also, you've heard the quartet album "Four of a Kind?" Yeah, that's the same Mark Lawrence. He's also one of the nicest folks I've met.